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9 papers · 2 filters
Permutations sortable by two stacks in parallel and quarter plane walks
Michael Albert, Mireille Bousquet-Mélou
At the end of the 1960s, Knuth characterised the permutations that can be sorted using a stack in terms of forbidden patterns. He also showed that they are in bijection with Dyck p…
Quasi-symmetric functions as polynomial functions on Young diagrams
Jean-Christophe Aval, Valentin Féray, Jean-Christophe Novelli +1
We determine the most general form of a smooth function on Young diagrams, that is, a polynomial in the interlacing or multirectangular coordinates whose value depends only on the…
Domination game: effect of edge- and vertex-removal
Boštjan Brešar, Paul Dorbec, Sandi Klavžar +1
The domination game is played on a graph by two players, named Dominator and Staller. They alternatively select vertices of such that each chosen vertex enlarges the set of…
Spanning forests in regular planar maps
Mireille Bousquet-Mélou, Julien Courtiel
We address the enumeration of p-valent planar maps equipped with a spanning forest, with a weight z per face and a weight u per connected component of the forest. Equivalently, we…
Combinatorics of non-ambiguous trees
Jean-Christophe Aval, Adrien Boussicault, Mathilde Bouvel +1
This article investigates combinatorial properties of non-ambiguous trees. These objects we define may be seen either as binary trees drawn on a grid with some constraints, or as a…
Asymptotic properties of some minor-closed classes of graphs
Mireille Bousquet-Mélou, Kerstin Weller
Let A be a minor-closed class of labelled graphs, and let G_n be a random graph sampled uniformly from the set of n-vertex graphs of A. When n is large, what is the probability tha…